PRMIA 8010 Exam - Topic 4 Question 52 Discussion

Actual exam question for PRMIA's 8010 exam

Question #: 52
Topic #: 4

[All 8010 Questions]

A bank extends a loan of $1m to a home buyer to buy a house currently worth $1.5m, with the house serving as the collateral. The volatility of returns (assumed normally distributed) on house prices in that neighborhood is assessed at 10% annually. The expected probability of default of the home buyer is 5%.

What is the probability that the bank will recover less than the principal advanced on this loan; assuming the probability of the home buyer's default is independent of the value of the house?

AMore than 1%

BLess than 1%

CMore than 5%

Show Suggested Answer

Suggested Answer: B

Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the loss distribution. In very simple and non-technical terms, EVT says the following:

1. Pull a number of large iid random samples from the population,

2. For each sample, find the maximum,

3. Then the distribution of these maximum values will follow a Generalized Extreme Value distribution.

(In some ways, it is parallel to the central limit theorem which says that the the mean of a large number of random samples pulled from any population follows a normal distribution, regardless of the distribution of the underlying population.)

Generalized Extreme Value (GEV) distributions have three parameters: (shape parameter), (location parameter) and (scale parameter). Based upon the value of , a GEV distribution may either be a Frechet, Weibull or a Gumbel. These are the only three types of extreme value distributions.

by Rashad at Jul 06, 2024, 08:22 AM

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Lacey

4 months ago

5% default probability is pretty low, but still risky!

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Dalene

5 months ago

Wait, how can they assume independence? Sounds off.

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Peggie

5 months ago

Definitely more than 1% chance of losing money here.

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Maryann

5 months ago

I think the default risk makes it more complicated.

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Alfred

5 months ago

The house is worth $1.5m, so recovery seems likely.

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Lilli

6 months ago

I think the answer might be less than 1%, but I’m not completely confident. We should consider both the default probability and the potential drop in house value.

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Louis

6 months ago

I feel like the probability of default is straightforward, but I’m uncertain about how the volatility affects the overall probability of recovering less than the loan amount.

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Trina

6 months ago

This question seems similar to one we practiced where we had to assess recovery rates. I think the key is understanding how the house value impacts recovery.

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Monte

6 months ago

I remember we discussed how to calculate the expected loss in case of default, but I'm not sure how to factor in the house value volatility here.

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Freeman

6 months ago

I'm not totally sure about this one. I might need to review some probability concepts before diving in. Better safe than sorry.

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Arthur

6 months ago

No problem, I've got this. Piece of cake. I'll just plug the numbers into the formula and boom, answer.

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Kip

6 months ago

Okay, I think I've got a strategy for this. I'll need to calculate the probability of the house value dropping below the loan amount, given the volatility and default probability.

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Mirta

6 months ago

This looks like a tricky probability question. I'll need to think through the key assumptions and variables carefully.

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Man

6 months ago

Hmm, I'm a bit confused by the wording here. I'll need to re-read the question a few times to make sure I understand what they're asking.

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Sueann

6 months ago

I'm leaning towards B. If the classification method makes it easy to place jobs into the right categories, that seems like a big advantage.

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Irving

6 months ago

Option D seems fine to me because it states a factual observation about the suspect's contradicting statements during questioning.

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Lynelle

11 months ago

Wait, wait, wait... the bank is lending a million bucks on a house worth $1.5 million, and the volatility is 10%? What kind of bank is this, the Bank of Risky Business? I'd be more worried about the bank losing their shirt than the home buyer defaulting!

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Lili

10 months ago

The bank must have a high risk tolerance to make that kind of loan.

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Stephen

10 months ago

I agree, the bank is taking a big gamble with that loan.

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Della

10 months ago

I know, right? That seems like a risky move by the bank.

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Leonora

11 months ago

Man, this question is making my head spin. Volatility, default probability, and all that math? I'm just going to go with the safe answer: D) 0. The bank will always get their money back, right? Easy peasy!

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Gearldine

10 months ago

User1: Hmm, you might have a point. Let's think this through a bit more before making a final decision.

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Breana

10 months ago

User2: I'm not so sure, what if the house value drops significantly? Maybe we should consider the other options.

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Kiera

11 months ago

User1: I think you might be right, D) 0 sounds like the safest bet.

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Merilyn

11 months ago

This is a tricky one. The bank is lending $1m on a $1.5m house, so there's some cushion. But with 10% volatility and 5% default probability, I'm betting the bank will recover less than the principal more than 1% of the time. I'll go with A) More than 1%.

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Whitney

11 months ago

I'm not so sure, I think the bank has enough cushion with the house value. I'll go with D) 0.

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Tran

11 months ago

I agree, the volatility and default probability make it likely that the bank won't fully recover the loan amount.

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Lacey

11 months ago

I think the bank will recover less than the principal more than 1% of the time.

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Jenise

12 months ago

Hmm, I'm not too sure about this one. The high volatility and probability of default make me think the bank might recover less than the principal more often than 1% of the time. I'll go with C) More than 5%.

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Cassi

12 months ago

I'm not sure, but I think the answer is D) 0 because the default probability is only 5%.

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Krystal

12 months ago

I agree with Brittney, the probability of recovering less than the principal seems very low.

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Vernice

12 months ago

This question seems pretty straightforward. I'll go with option B) Less than 1%. The volatility of house prices is only 10%, and the probability of default is 5%, so the bank should be able to recover the principal in most cases.

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